CHAPTER 7
LESSON 1
Teachers Guide
Experimental and Theoretical Probability
Objectives:
 Distinguish between experimental and theoretical probability.
 Define (theoretical) probability.
 Find basic probabilities by counting favourable outcomes.
 Use tree diagrams with equally likely pathways.
Example 1:
Visualize rolling a die.
a) What is the theoretical probability of getting a 5?
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Visualize
P
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=
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1
6
b) Simulate rolling a die 300 times and recording the number of times a 5 appears. From your
simulation, what is the experimental probability of getting a 5? Compare this probability with
the theoretical probability.
1
Rand Bin (1, ,300)  L1
(* to get Rand Bin press MATH
7)
6
Sum (L1) = “54”
( to get sum ( L1) press LIST
5 (L1) )
 “experimental” probability =
e.g.
Example 2:
Suppose one card is drawn from a deck of 52 cards.
What is the probability that it is
a) a face card?
P (face card) =
b)
12
52
a red ace?
P (red ace) =
2
52
Club
K
Q
J
10
9
8
7
6
5
4
3
2
A
*
*
*
*
*
*
*
*
*
*
*
*
*
54
= 0.18
300
Diamond Heart Spade
*
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*
*
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*
*
*
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*
*
*
*
*
*
*
*
*
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Probability
If an experiment has n equally likely outcomes of which r outcomes are favourable to event A,
then the probability of event A is:
P A 
r
n
Calculating Probabilities Using Tree Diagrams with Equally Likely Branches
Example 3:
What is the probability that in a family of 3 children there are exactly 2 girls?
1st child
Solution Steps:
Draw a tree diagram to represent the possible
arrangements of boys and girls in a family of 3
children. Each branch (pathway) is equally likely.
Why (assumptions)?
G & B – equally likely at birth.
2nd Child
Determine the number of
branches that contain 2 girls. (3)
G
B
B
G
B
G
3rd. Child
Divide that number by the
total number of branches to
determine the probability that
there are 2 girls in the family.
3
P(2girls) =
8
B
G B
GB
BGG
G
B
GBG GGB
G
Example 4:
When the pointer is spun twice, find the probability that (tree)
a) you win a total of $10 .
$5
$0
$10
$20
1st Spin
5
0
2nd Spin
0
5
10
20
0
20
10
5
P(total = $10) =
20
10
0 5
10
20
0
5
16 equally pathways
20
10
3
= 0.1875
16
b) the same number comes up on each spin.
*
Could also do a table
4 pathways give same # on each spin.
{ (0,0), (5,5), (10,10), (20,20)}
4
1
=
P(same # on each spin) =
16 4
0
5
10
20
0
( 0, 0)
( 0, 5)
( 0, 10)
( 0 , 20)
5
( 5, 0)
( 5, 5)
( 5, 10)
( 5 , 20)
10
( 10, 0)
( 10, 5) ( 10, 10)
( 10, 20 )
20
( 20, 0) ( 20, 5) ( 20, 10)
(20, 20 )
Example 5:
When two bills are randomly selected from the pot without
replacement, find the probability that you win a total of $10.
* intuitively – do you think this is higher or lower than eg.4
could do tree
or table
0
5
20
10
5
10
20
0
10
(0,10)
 P(total#10) =
2 1
=
12 6
20
0
5
20
(10,0)
0
10
5
$0
0
$5
$10 $20
0
5
0
x
(0,5)
( 0 , 10 )
( 0 , 20 )
5
(5,0)
x
( 5 , 10 )
( 5 , 20 )
10
( 10 , 0 )
20
( 20 , 0 )
( 10 , 5 )
10
x
( 20 , 5 ) ( 20 , 10 )
20
( 10 , 20 )
x